Question: Solve for $x$ : $x^2 + 13x + 40 = 0$
Explanation: The coefficient on the $x$ term is $13$ and the constant term is $40$ , so we need to find two numbers that add up to $13$ and multiply to $40$ The two numbers $5$ and $8$ satisfy both conditions: $ {5} + {8} = {13} $ $ {5} \times {8} = {40} $ $(x + {5}) (x + {8}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 5) (x + 8) = 0$ $x + 5 = 0$ or $x + 8 = 0$ Thus, $x = -5$ and $x = -8$ are the solutions.